12th Graders Head Back To Middle School Math

Andy Wight gathered high school seniors into a circle and unveiled the title of their new textbook: “PreAlgebra” by Elayn Martin-Gay.

“I took prealgebra in middle school,” groaned one student.

The student, who is set to graduate this spring from Hill Regional Career High School, is among 169 New Haven public school 12th-graders who got a spring-semester surprise: Before they can go to college, they have to go back to pre-algebra.

In other words, they have to do middle-school work before they can advance to higher education.

And it turns out some of the students, who have been promoted all the way through high school, need to do that. Some of them haven’t absorbed basics like multiplication tables. Some have trouble adding or subtracting without a calculator.

Seniors at all 11 district high schools got the surprise in January as the New Haven public schools rushed to prepare for a new state law. The law, Public Act 12-40, which the governor signed in 2012, shifts the burden of remedial education from state colleges and universities to high schools. That means that starting in the fall, Gateway Community College, the most popular destination for New Haven public school grads, will stop offering its lowest-level remedial classes, Math 075 and English 043, to incoming students who need to catch up in English and math.

The school district concluded that, based on kids’ SAT scores, about half of the city’s high school seniors may need to take remedial math or English classes before earning credit in college. Since the colleges won’t offer remedial classes in the fall, students need to catch up before then—or face being barred admission to even their local community college.

As a last-minute intervention, Gateway has offered New Haven a one-time deal for this spring: The college teamed up with the public schools to create English and math classes at all 11 city high schools that mimic the remedial classes at Gateway. Students who get a C or higher in the classes will automatically test out of Gateway’s remedial requirement—enabling them to enroll in developmental-level courses at the college in the fall, and potentially start learning other subjects.

Dolores Garcia-Blocker, the school system’s new director of college and career pathways, said the new courses aim to help students who, because of the new law, might otherwise find themselves unable to attend their local community college next fall.

The city expects to graduate over 1,000 students in June, she said. “We didn’t want to be graduating them to nothing.”

Students were identified as in danger of not being able to go to college if they earned less than a 400 in math, or less than a 410 in English reading or writing, on their SAT. A total of 550 fell into that category. Of those, 474 and enrolled in the new, Gateway-aligned “refresher” classes this spring: 169 are taking math and 382 are taking English.

The new experiment drew nine seniors last week into a second-floor science lab, where teacher Andy Wight was kicking off one of the special catch-up courses in math.

At the beginning of the course, he gave them a “pre-test” of 6 problems that illustrate the range of math expected in the course.

The first question: What is 12 + 16?

Second question: Simplify 47 ÷ 34.

(Scroll to the end of the story for the answers to the six questions displayed in the two boxes; see if you know them.)

Students were asked to do these questions without a calculator.

“Nothing here should be of great challenge to high school seniors,” Wight said, “yet we have so many who cannot do mathematical calculations of this type with confidence.”

The content of the material came as a surprise to seniors, who had been chugging along in higher math classes.

After four years of high school, why were they suddenly taking “middle-school math”?

All students had already taken pre-algebra. Students who placed into Wight’s class had all moved on to higher classes, including Algebra II, statistics and even pre-calculus.

But somehow, they passed through the system without absorbing the fundamentals of math, Wight explained in an interview.

There are students who pass Algebra II, but still can’t add, subtract or divide without a calculator, Wight said. They don’t know their times tables. And they have trouble with problems with percents.

After testing students, Wight unveiled the syllabus for the class. It started with the very basics: place value, the difference between the tens and the hundreds place. It moved on to multiplying whole numbers (maximum of 3-digit numbers times 2-digit numbers). A note on the syllabus reads: “Drill mult. tables.

Wight covered Chapter 1 before the new books came. Last week, he distributed the books and had students turn to Chapter 2, on integers. (An integer is 0,1,2,3, etc., as well as -1, -2 -3, etc.) The syllabus calls for adding and subtracting these types of numbers, up to three digits long. (E.g.: 100 minus -203.)

He told students to open the book to Chapter 2. For homework, they would have to do every other odd number.

To check comprehension, he had students go around the room counting off every other odd number: 1, 5, 9, 13, ...

One student shook her head before her turn even came. “No. I can’t do it,” she said, sounding discouraged.

Wight later said that kind of lack of confidence with basic numeracy is one obstacle the class will aim to overcome.

By the end of the course, students will reach problem-solving with percentages, including sales tax, discounts and commissions.

Wight spent some time selling seniors on the idea.

He encouraged them to ignore the title of the text book. It shouldn’t be called “pre-algebra.” It should be called “life skills math,” he offered. He said students already know a lot of these skills, but may have forgotten them. Taking the class will be like hitting the “refresh” button, and recalling important fundamentals.

“Adding 2 plus 2 does matter,” he told the class.

He handed out a cartoon that aimed to show that the place value of a number matters, too. The cartoon showed a wily corporate exec who gives himself a pay-raise of “0,” from $80,000 to $800,000.

“If you go out of high school and you can’t combine [like terms] or subtract, you’re going to be used and abused by somebody who takes advantage of your lack of knowledge,” Wight reflected in an interview.

Wight told his class that he wouldn’t spend the semester quizzing them on their times tables. But “we’re trying to make sure that doing the times table is something you’re confident doing.”

Maryy Domes (pictured), who plans to study business management at Southern, professed confidence in passing the class. The Gateway course won’t give students credit at Southern, but it aims to bring them up to speed so that they can score well on a placement exam.

Students said they aim to enroll in Gateway, Eastern Connecticut College, Albertus Magnus, or the U.S. Air Force.

“Shaky Foundations”

The number of high school seniors who need help with middle school math and basic English is “alarmingly high,” said Garcia-Blocker. “But I’m not surprised.”

“Why? We don’t have really clear understanding of what readiness at the next level looks like. If you don’t know what it looks like, you don’t know how to prepare kids for it,” Garcia-Blocker said.

Schools Superintendent Garth Harries said the need for senior-year refresher courses presents a “wake-up” call for the school district and the city. He said it also highlights key areas in which the school system and college system are not aligned: For example, the state’s high school curriculum allows kids to use calculators in math class; the state college and university entrance exam, the Accuplacer, does not.

A study in 2011 found that 89 percent of the New Haven Public School graduates who enrolled at Connecticut public colleges and universities needed to take remedial or developmental classes in English and math before they could start earning credits. That fact can be costly: Students end up burning through their federal financial aid to take non-credit-bearing refresher courses before they can even start making progress towards a degree.

Wight (pictured), who has taught math for 28 years, called students’ lack of math basics a longstanding problem.

“My math colleagues and I consider it appalling that 60-plus percent of New Haven high school graduates need remediation,” he said. “We have long been aware of this and have tried to figure out ways to address the real needs within the curricula we are supposed to teach.”

Many students “don’t have the mathematical fundamentals that every student should know coming out of middle school,” he said. Wight said students may learn the math skills for a particular course, but “skills are not being retained.” Teachers should “embed skill review in every level” of math to ensure that doesn’t happen, he said.

Garcia-Blocker said she observed the problem in her former role as principal at Cooperative Arts and Humanities High School.

“I would sit in math classes, from Algebra I lab to the highest-level” classes. When kids would get a problem wrong, she said, it would often “boil down to the real lack of understanding with their basic math facts.”

“If kids don’t have a basic understanding, it’s hard to layer on the more complex math,” she said. In the current high-school system, which is based on seat time instead of mastery of a subject, students can skate through school with Ds and make it to advanced math classes without mastering the basics.

“You get to senior year with kids with these very shaky foundations, because they really haven’t mastered the skills,” Garcia-Blocker (pictured) said.

Several city high schools, including High School in the Community, are changing to a “mastery-based” system, where kids have to demonstrate they know how to each skill—such as factoring polynomials or finding the length of the hypotenuse—before moving on. In that system, kids move onto the next chapter—and the next course—at their own pace, when they’re ready. The system aims to ensure that a high school diploma “means something.”

“People were outraged that those freshmen were retained,” Garcia-Blocker said. But she said the school—and a few others in town—are taking on an important shift towards ensuring kids are learning the skills they need to be successful in college and life.

A Rushed Rollout

At Career High, a magnet high school on South Frontage Road, 75 of 158 seniors found out in January that they had to take “refresher” courses in math or English, according to Principal Madeline Negron. Thirty-seven are enrolled in math classes like Wight’s.

The classes were a last-minute fix: The school found out in December that it would have to make the classes available the following month. That posed a major scheduling challenge. Students were pulled out of 11 different math classes into three new “refresher” courses, according to Wight.

The feeling was urgent: “We’ve gotta do this now or you’re screwed” after high school, Wight said.

Staff were “a little flustered” by the reshuffling, Negron said.

“The process wasn’t as smooth as we might have preferred,” said Negron, “but we have to be thinkers,” problem-solvers.

Superintendent Harries said the process was so rushed because the district didn’t come up with the idea of offering a Gateway-aligned course until last fall, after school had already started. He said the district had previously been working on “broader responses,” such as aligning the curriculum to the Common Core State Standards; offering students dual-enrollment or “middle college” programs; and new self-paced, mastery-based programs like the one at HSC; and better systems to track kids’ success in high school and college.

The refresher courses, meanwhile, arose from “recognizing the immediate situation that these students were facing.” Gateway is the most common destination for New Haven public school graduates, Harries said.

Some Lobby Against “Unfair” Law

Public Act 12-40 aims to ensure students are finishing high school ready for college. And it aims to prevent kids from spending money on remedial classes before they even get the chance to start earning college credit. Students who enroll in remedial classes are much more likely to drop out. The full law calls for high schools and colleges and universities to align their curricula.

Critics have been lobbying Hartford to address what they call an unfair discrepancy in the law: Colleges and universities are required to yank their remedial classes in 2014, two years before the law requires high schools to establish curricula that will prepare them for college. (Click here to read the Reg’s Rachel Chinapen’s recent story about a public hearing in Hartford.)

Wendy Samberg, director of instructional design at Gateway, called the law “unfair and immoral” because it “disenfranchises low-performing students without a plan in place to address the issue.” Gateway’s two remedial classes are popular: Some 1,155 students per year take Math 075 and 750 take English 043, according to Samberg. She said it’s unfair to pull the plug on those classes while students’ high-school classes still are not aligned with college coursework.

“PA 12-40 puts students in great jeopardy,” Samberg wrote in an email. She said some Gateway officials are working with legislators to delay the requirement that colleges drop their remedial classes.

In an interview Tuesday, Gateway President Dorsey Kendrick took a more diplomatic stance.

“We’re going to honor the law,” she said. She said she wanted to “stay out of the politics”; she will let the Board of Regents determine whether parts of the law should be delayed.

Superintendent Harries called the law “totally appropriate and frankly important.” Districts “should ensure that a high school diploma has maximum meaning,” he said. “The law is mobilizing and motivating good steps in that regard.”

However, he said, “I think the timing and the impact on students who haven’t had a lot of run-up to the implementation of this is a challenge.”

Garcia-Blocker, the public schools college readiness chief, said the district is “about to embark on a longer-term strategy” to “align what we are doing in high school to the expectations of college.”

“That work has not been happening” until now, she said. She said she will be sitting down with representatives from Gateway, SCSU and UConn to talk about what skills New Haven public school grads are missing when they show up in college.

Meanwhile, Kendrick said Gateway is working on ways to ensure that students won’t be barred access. While Gateway is required to stop offering its lowest-level remedial classes, Math 075 and English 043, the school is working with community partners to offer a computer-based course that would address some of those fundamentals, she said. Students will still be allowed to take a remedial “boot camp” class over the summer, and to take second-level developmental courses for one semester before enrolling in credit-bearing courses, she said.

“I do not want any child or any adult to be locked out of being able to offer their full potential,” she said. Now for the answers to the two questions at the top story:

First question: 28

Second question: This looked like a trick question to this reporter, because you can’t reduce the fraction 47/34, because 47 is a prime number. However, Wight said the answer is 1 and 13/34, because a mixed fraction is considered more simplified than an improper fraction. The answer 1.382 is acceptable, too, he said.

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Comments

posted by: Champ358 on March 4, 2014 6:57pm

While it is a good thing that NHPS system is scrambling to prepare children for college, how is it that they only just discovered the problem? How is it possible that a significant percentage of 12th graders do not know the multiplication tables?

posted by: heightster70 on March 4, 2014 8:23pm

Is this the best we can get out of a 400 million dollar budget? New Haven BOE is all smoke and mirrors

posted by: naturaleza on March 4, 2014 8:29pm

“How is it possible that a significant percentage of 12th graders do not know the multiplication tables?”

Sometimes state testing requires teachers to plow through a high volume of material, and students are not able to gain a proper foundation. Also, remember that a grade of D- will get you to the next level. Cs and Ds in middle school turn into Ds and Fs in high school, and that crushes self-confidence and motivation. Expectations are suddenly reduced by teachers, and good behavior gets you a passing grade. High-stakes state tests (which don’t directly benefit students) only confound the problem.

posted by: NewHavenPublic on March 4, 2014 8:30pm

“Superintendent Harries called the law “totally appropriate and frankly important.””

It’s “appropriate and important” to deny community college seats to graduating seniors from New Haven high schools? Please explain your position, Mr. Harries.

posted by: Samuel T. Ross-Lee on March 5, 2014 4:43am

How is it possible that High School students, past and potential High School graduates, do not know the multiplication tables? Well, let’s see.

I think we can safely assume that this situation didn’t start yesterday, or this academic year. And, if that assumption is correct, and we ALL know that it is, then we can further conclude that many people at all levels of the NHPS system were aware of this fact YEARS ago, from the Superintendent to the faculty, not to mention the former despotic Mayor who controlled the BOE and used it as a political football, hiring people in it who would contribute to his campaign and shut up about the inadequacies of its product.

So, while the media, including but not limited to this “independent” publication, was focused like a laser on a dispute between the former Mayor, a principle and a person on his staff, they were (intentionally?) ignoring the larger issues of under-educated, largely African-American, youth being handed HS diplomas that meant nothing, as these “graduates” couldn’t do the math taught to middle school students.

The number of public officials involved in this travesty is down right criminal. The number of African-American faculty and administrators who knew (and know) about this and refused, for the sake of their jobs, positions, middle-class status, and lack of courage, to speak out is down-right sinful.

And, the fact that the new Superintendent, who was a part of the old regime, is trying to turn this preventable malady around on a dime, punishing the students caught in a system not to THEIR making, while the adults who caused the problem will face NO repercussions is at least shameful and unfairly punitive.

posted by: Teacher in New Haven on March 5, 2014 7:33am

The news here is NOT that half of New Haven Seniors are not ready for college math. Anyone who has been paying any attention for the last 10 years knew that already.

The news here is that NHPS and Gateway are finally trying to do something about it systemically.

posted by: Teacher in New Haven on March 5, 2014 9:32am

I can’t see how asking students to learn something they have not yet learned amounts to punishment.

Furthermore, it is not within the power of the current superintendent to punish the previous superintendent, the former mayor, the community, parents, former students, the state, the funding structure, property taxes, Yale or the vast majority of the many many people responsible for this historic failure.

It took a law at the state level, and a new superintendent to see change on this front, and I for one applaud it.

posted by: AMI1 on March 5, 2014 9:51am

the losing of the remedial program at the Community College level is short sighted. While I applaud getting the incoming class of high school graduates up to speed prior to getting to the Community College, what about the returning adult students who may have never acquired those basic skills or have atrophied over time. Our community college system serve a much larger population than just incoming recent HS grads.

posted by: Bishop on March 5, 2014 9:52am

@Teacher in New Haven “The news here is that NHPS and Gateway are finally trying to do something about it systemically.”

I’m with you on the new standard, but I feel like this is a band aid and not a solution. The reality is that even if this program is wildly successful, a whole chunk of NH graduates will only be proficient in 8th grade math. That’s hardly closing the opportunity/achievement gap. What we really need to do is up expectations across the board for administrators, teachers, students, and families.

It’s not often that I agree with Rev. Ross-Lee on issues, but I am 100% behind the spirit of his comments. This is an absolute disgrace - the urgency we need to feel about this is palpable and real. These are real children with real lives as stake, and if we don’t shake up this system fast (the nature of that shakeup potentially would provide a more contentious discussion :), we are talking about thousands of our children that will be shut out from the jobs of tomorrow.

posted by: Jeff Klaus on March 5, 2014 10:05am

I commend the district for finally acknowledging the situation and taking some action. Bravo.

posted by: matticus on March 5, 2014 10:35am

I remain unconvinced that 1 13/34 is a simplified version of 47/34. To perform any mathematical operation one would need to convert the mixed numeral to the improper fraction first, then proceed with the operation. Additionally, the writer states 1.382 is also acceptable. 1.382 is NOT 47/34. 47/34 represents an irrational number, meaning when the fraction is dived out, the places beyond the decimal point run on without end. 1.382 In fact represents a close approximation to 47/34, but it is indeed not the same value as 47/34. Am I alone here, or can someone verify? NHI, help?

posted by: Brutus2011 on March 5, 2014 11:10am

to ‘Matticus”

As a former math teacher, I would agree that 1 and 13/34 is an acceptable answer. It is most important that a student recognize a prime number, in this case in the numerator and unless the denominator is either one or the number in the numerator then only a decimal will result. Therefore, expressing the fraction as a mixed number is appropriate for a pre-algebra level.

to “Samuel T. Ross-Lee” and “Bishop”

Right on!

posted by: Teacher in New Haven on March 5, 2014 11:18am

Bishop

You are right on. This is a band-aid. The real question becomes, what will change next year for a student who is failing math as a junior or an 8th grader.

This is the first step. If it is the only step it will be a travesty. If it is the first step of many, then I am on board.

posted by: matticus on March 5, 2014 12:43pm

To Brutus:

I think the problem is insufficient to test whether students can identify a prime number. Take for example the improper fraction, 35/34. 35 is not a prime number, but the fraction could be expressed as 1 1/34. I think I largely take issue with the direction, “Simplify”. I would have used the term “Express as a proper fraction”. I would be interested in your take on 1.382 as an acceptable simplification.

posted by: Brutus2011 on March 5, 2014 1:31pm

To “Matticus”

I respectfully submit that a teacher must keep in mind the appropriateness of the lesson(s), etc.

In this case, I believe what you wish to discuss is “not-appropriate” for students in pre-algebra—especially with those who likely have math insecurities, etc.

I would be happy if the kids knew the difference between proper fractions, improper fractions, and mixed numbers and could convert them etc.

Depth of learning is one thing but these kids are in 12th grade but on a 6th-7th grade math level—gotta engage them and not spook them. Only my opinion of course. Perhaps other math teachers could weigh in here.

posted by: Melissa Bailey on March 5, 2014 1:32pm

Matticus—I totally agree with you: The rounded decimal loses information and is not the same as 47/34. And mixed fractions such as 1 13/34ths are useless if you’re going to do anything further with the number. I would argue that 47/34 is a perfectly acceptable answer. 1 13/34 is not wrong, though.

posted by: WestvilleCitizen on March 5, 2014 5:42pm

@matticus Since you asked… a rational number is any number that can be expressed as a fraction of two whole numbers (a “ratio”). So 47/34 despite your character assasination :) is INDEED quite rational (it is in fact precisely represented using 12 decimals). In contrast, irrational numbers cannot be represented as a ratio between two whole numbers or a finite number of decimals. Thus the mystery of pi and the square root of 2 to the ancients. The ratio of the circumference of a circle to its diameter - or the mystery of the ratio of the length of the diagonal of a square to its side (the square root of 2). Both are palpable concepts right before our eyes, and both resist all attempts to be expressed precisely as a simple ratio of whole numbers. More importantly, thank you to these teachers and administrators for trying to right a wrong and lend a hand at numeracy to our soon-to-be graduates.

posted by: Don in New Haven on March 5, 2014 6:16pm

Simplify 47 ÷ 34.

When I read this question my immediate thought was that here is another example of why American kids fail to know math. Simply stated, this is a dumb distraction question not intended to teach anything of value. Young minds should not be told to deal with math questions that provoke endless discussion concluding with nothing. This wastes their time in class and alone outside of class. How many minutes of class time would a teacher waste on a worthless question like this? No doubt this is a multiple choice test and the test taker may guess without learning anything. When asked to simplify, the result should be readily recognized by anybody. Check the comments on this page to see that there is no agreement on this question result. Questions like this cause kids to give up on math studies. If it is important to deal the numbers 47 and 34, a word question such as the following could be used: There are 47 girls and 34 boys in the eighth grade. How many students are in the eighth grade?

posted by: NewHaven06513 on March 5, 2014 7:37pm

Bravo to the students and teachers in this article! Take control of your future! This is the end result of a generation who is more interested in their cell phones and Facebook than school… Parents who aren’t ready to parent and a failed education system. Education is not always a priority in every home. Parents set a time and place nightly for your children to do their homework. Do it with them and communicate with your teachers. We’re all in thus together! Teachers, challenge your students and hold them accountable ?

posted by: nhmathteacher on March 5, 2014 8:28pm

So many issues—political and pedagogical are touched on by this article that it is no surprise that reader comments are diverse. Bottom line: it is appalling that many high school grads are so weak in numeracy; it is good that some action is being taken; this is only a one year emergency intervention—real planning for change was and is still needed. Thankfully no one has jumped in to blame the teachers, but as one who has been trying to address math learning for years, I do share some responsibility. Change is needed, guess it starts with me. Meanwhile, the discussion of what constitutes a ‘good’ or correct answer to the problem of 47 divided by 34 is fascinating. Please bear in mind that this is a question in the context of the start of a prealgebra curriculum. It is not multiple choice, it is not presented as a fraction (47/34), it invites student responses which the teacher would need to interpret as pointers to depth of student understanding of division notation, division process, division outcomes. The real disservice to learning and rise of student discouragement comes from thinking there is only one real, true answer to any math problem. I would be much more interested in hearing how students justify the logic of whatever they answer. That is the path to lasting numeracy.

Gateway CC is a Godsend for so many—thanks for all you do—about 35 years ago, students had to qualify by grades and tests to get into college—and therefore mainly only the elite could attend—then higher education across the nation decided to let mostly all children attend college (but they had to take remedial courses)—and these courses cost $$$—but now everyone can attend college—and if they can’t pass these courses they are dismissed—I think it was a good decision to let all students attempt higher education—but the $$ disturbed me a bit—In urban and suburban education throughout the country many students don’t learn what they should have or need to during their high school years for a plethora of reasons—that has how it always has been and always will be—(for it is the students choice to participate in their education or opportunities)—not all decide to participate and others just don’t have the ability—I am very excited about this move in New haven to go back and teach the basics—we have all talked about this for ages—and now it has become real—Thanks, Dr. Garcia-Blocker and Mr. Wight and all you other teachers participating—and thank you Ms. Kendrick (Prez of Gateway)—you are a shining star and have been one for quite some time—Tom

I need to comment again as I just read the other comments—This is the best thing ever—lets go back and get it right for those students who weren’t ready to get it at the time they were taught the subject (many of those students have matured since then and deserve the chance at a strong foundation in the basics of Math)—I am so proud of our district leaders to address this problem w/o fear—you are champions—(Ken Mathews, Imma Canelli, Garth Harries, Dolores Garcia-Blocker)—Wow—this is great stuff—Thank you—my own kids in the suburbs could use this refresher for sure—Awesome, and while we are at it why don’t we offer these courses to all our parents who may have not mastered the basics—our education system must be here for all of our community whether they are 3 or 103—-and I know we all believe this—join the movement—it’s exciting and participating is fun and worthwhile—there are so many avenues for everyone to get involved—we need you parents and guardians to tell us what you want and to assist us in getting us to where you want us to go—Tom

posted by: andywight on March 6, 2014 8:58pm

Students I have interviewed at my school feel insulted by the article’s title. They do know multiplication tables and do not feel they are going “back” to middle school math. Setting aside Tom Burns’ gushing praise of the administrators who came up with this intervention at the last minute, he may have a good point that student maturity makes a huge difference. Though they once learned these math lessons and left them behind, they are now able to think about how to solve problems and bring new understandings to basic, necessary operations. Metacognition is wonderful thing!

posted by: Westville voter on March 7, 2014 11:57am

College bound students who don’t know basic math. This is not something that happened suddenly. This is a product of years of failure to address obvious issues. I’m glad that these kids are getting the help they need. It’s not their fault that their school has simply passed them up the ladder while failing to educate them. How about some explanation for how this happened and some consequences for those who failed these kids? They are Reggie Mayo’s real legacy. Shame on NHPS!

posted by: Westville voter on March 7, 2014 1:55pm

While we are passing out blame/shame for this systemic failure, everyone should also note that education is not even mentioned in the UNITE bloc’s 2014-15 citywide agenda. NOT EVEN MENTIONED!!!!! The BOA is AWOL on this issue as well and is not even pretending to care. Shame on them! Confront them and demand answers, action, and apologies to our children for abandoning their future. We deserve so much better than this!

Years ago my daughter was a student at Coop High School (former campus on Orange St.). Due to a chronic health condition she was enrolled in a 504 plan. She took pre-calculus but the teacher didn’t want to bother with creating a plan for her so, even though she never attended a single class, never handed in a single assignment, never took a single test—she received an A. When she took an online math placement test for her college she flunked at the basic arithmetic level. The story ultimately had a happy ending: she graduated college with 2 degrees but had to take each college math course repeatedly to get passing grades.